I have my dad's old snare drum, a practice pad, a pair of sticks, and Buddy Rich's book of rudiments. I'd like to get better at jazz drumming, because I occasionally have to for a band I'm in. Currently, I can play a simple beat with 3 limbs - e.g. bass on 1 and 3; high hat on 2 and 4; and swung quavers on the ride or playing the snare (but not both). Are there ways to use the snare to practise this kind of coordination, as well as rudiments?
To an extent, you can practice on anything which has the right kind of 'bounce back' for the sticks. You don't even need that iof you're just practicing getting things in the right order.
It helps if you have two objects with different sounds, so you can hear differences if practicing strokes between the two, eg like a paradiddle etc. However for practicing the mechanics of drumming (with hands- not feet), you don't need any particular sound; you can just have a couple of pads or a snare and a hi-hat or something. This is fine for practicing the rudiments.
On a snare, you can get loads of different sounds by hitting it in different places on the skin (try right near the edge vs. right in the middle, and all the way along) and sidestick on the snare rim of course.
However for bass drum technique and overall 'oomph' you're better off with something that sounds a bit like a kit, even if it's just a practice kit or even an electronic one, so that you have a clue how hard to hit things to get the right noises.
Also tapping your foot is ok for marking when you'd play a bass drum but there's a lot of variety of techniques involved in actually playing a bass pedal so it might feel odd when you come to play a kit.